The coordinate-wise core for multiple-type housing markets is second-best incentive compatible

Abstract

We consider the generalization of Shapley and Scarf's (1974) model of trading indivisible objects (houses) to so-called multiple-type housing markets. We show that the prominent solution for these markets, the coordinate-wise core rule, is second-best incentive compatible. In other words, there exists no other strategy-proof trading rule that Pareto dominates the coordinate-wise core rule. Given that for multipletype housing markets Pareto efficiency, strategy-proofness, and individual rationality are not compatible, we show that applying the coordinate-wise core rule is a minimal concession with respect to Pareto efficiency while preserving strategy-proofness and individual rationality.

Roth–Postlewaite stability and von Neumann–Morgenstern stability

“…12 On the other hand, Wako (2005) shows that the CWCA is the outcome of a coalition-proof Nash equilibrium of a simple strategic form game. Klaus (2008) shows that the CWCA allocation is second-best in that it is not Pareto dominated by any other allocation method that is strategy-proof. Anno and Kurino (2014) extend this result to general indivisible goods allocation problems with multiple types.…”

A dynamic recontracting process for multiple-type housing markets

“…We endow each agent with one commodity of each type (e.g., houses and cars or, more realistically, tutor groups for different courses as described in Klaus, 2008) and analyze simultaneous trade in all these types. Konishi et al (2001) show that the core of such an economy may well be empty or multi-valued.…”

Mechanism Design for Multi-Type Housing Markets

“…In this paper, we ask the following question: is it possible at all to design good mechanisms for multi-type housing markets? In multi-type housing markets (Moulin 1995;Konishi, Quint, and Wako 2001;Wako 2005;Klaus 2008), there are multiple types of items, each agent is initially endowed one item of each type. The goal is to design mechanisms without monetary transfer to (re)allocate items to the agents based on their preferences over bundles of items, such that each agent gets one item of each type.…”